 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
Archive of Issues
| Total articles in the database: | | 13217 |
| In Russian (Èçâ. ÐÀÍ. ÌÒÒ): | | 8152
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| In English (Mech. Solids): | | 5065 |
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| Saurav Sharma, Sangeeta Devi, Rajneesh Kumar, Ibrahim S. Elshazly, Imed Bachar, and Kh. Lotfy, "Investigation of Uniqueness, Reciprocity Theorems and Deformation in Multi-Phase-Lags Anisotropic Thermoviscoelastic Diffusion Model," Mech. Solids. 60 (2), 1289-1313 (2025) |
| Year |
2025 |
Volume |
60 |
Number |
2 |
Pages |
1289-1313 |
| DOI |
10.1134/S0025654425600242 |
| Title |
Investigation of Uniqueness, Reciprocity Theorems and Deformation in Multi-Phase-Lags Anisotropic Thermoviscoelastic Diffusion Model |
| Author(s) |
Saurav Sharma (University of Houston Cullen College of Engineering, Houston, Texas, 77054 USA, University of Houston Cullen College of Engineering, Houston, Texas, 77054 USA, sauravkuk@gmail.com)
Sangeeta Devi (Salarpura (Gheer), Karnal, Haryana, India, pin-132023, Salarpura (Gheer), Karnal, Haryana, 132023 India, sangeetakamboz@gmail.com)
Rajneesh Kumar (Department of Mathematics, Kurukshetra University, Kurukshetra, Haryana, India, rajneesh_kuk@rediffmail.com)
Ibrahim S. Elshazly (Department of Basic Sciences, Common First Year, King Saud University, Riyadh, 11451 Saudi Arabia, iali2.c@ksu.edu.sa)
Imed Bachar (Department of Mathematics, College of Science, King Saud University, Riyadh, 11451 Saudi Arabia, abachar@ksu.edu.sa)
Kh. Lotfy (Department of Mathematics, Faculty of Science, Zagazig University, Zagazig, Egypt, khlotfy_1@yahoo.com) |
| Abstract |
A new model involving the equations of thermoviscoelastic diffusion under multi-phase-lags for anisotropic medium (ATDM) is presented. The simulated model is obtained after modifying
the basic Fourier’s [1] and Fick’s [2] laws to involve the higher order time derivatives of heat flow vector, the gradient of temperature, diffusing mass flux, and chemical potential gradient. The governing
equations for the ATDM are considered to establish uniqueness and reciprocity theorems. By applying
the Laplace transform a uniqueness theorem for the considered model is proved and the reciprocity
theorem is derived. Instantaneous concentrated body forces, heat sources, and chemical potential
sources along with moving heat and chemical potential sources are taken to illustrate the applications
of the reciprocity theorem for a specific case. It has been recognized that these theorems are impacted
by the perceptivity of the involved field variable along with the variations of parameters involving
higher-order time derivatives. Also, the orthotropic thermoviscoelastic diffusion with a multi-phase-lags model for the one-dimensional case presents a deformation due to thermal and chemical potential
sources. As the application of the problem instantaneous thermal and instantaneous chemical potential sources are taken. Comparison has been made for Lord-Shulman (LS), dual phase lags, and higher
order time derivatives on displacement, stress, temperature, and chemical potential. Some unique cases are also established and correlated with known results. The effect of phase-lags plays an important role in processing and characterization to improve material properties and find applications in geomechanics, earthquake engineering, and the designing of new materials. |
| Keywords |
thermoviscoelastic, diffusion, anisotropic, multi-phase-lags, uniqueness, reciprocity theorem, and deformation |
| Received |
18 January 2025 | Revised |
15 February 2025 | Accepted |
26 February 2025 |
| Link to Fulltext |
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